The invention applies to rackets for sports such as tennis, racket ball, and squash, where conventional rackets have generally used a frame on a handle supporting a network of tension strands in a plane for hitting a ball. The invention involves recognition of the possibility for and advantages from forming the tension strand network with a double curvature in a saddle shape, and the invention aims at greater variety and enjoyment of racket sports by allowing a larger repertoire of shots and spin effects and providing a string network that is stiffer, more responsive, has a larger "sweet spot" or highly responsive area, and allows higher-velocity shots.